A Markov approach to characterizing the PK-PD
relationship of anti-migraine drugs
Maas, H.J.
Citation
Maas, H. J. (2007, June 5). A Markov approach to characterizing the PK-PD
relationship of anti-migraine drugs. Retrieved from
https://hdl.handle.net/1887/12040
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thesis in the Institutional Repository of the University
of Leiden
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A Markov approach to characterising the PK-PD relationship of anti-migraine drugs Hugo J. Maas
Ph.D. Thesis, Leiden University, June 2007
A Markov approach to
characterising
the PK-PD relationship of
anti-migraine drugs
Proefschrift
ter verkrijging van
de graad van Doctor aan de Universiteit Leiden, op gezag van Rector Magnificus prof.mr. P.F. van der Heijden,
volgens besluit van het College voor Promoties te verdedigen op dinsdag 5 juni 2007
klokke 13:45 uur
door
Hugo Maas
geboren te Roermond in 1977
Promotor : Prof. dr. M. Danhof Co-promotor : Dr. O.E. Della Pasqua
Referent : Prof. L. Aarons (University of Manchester)
Overige Leden : Prof. dr. E.R. de Kloet Prof. dr. J.M.A. van Gerven Prof. dr. A.P. IJzerman Dr. F.M. Spieksma
Contents
1 General introduction:
analysis of the treatment response of anti-migraine drugs in clinical trials 9
1.1 Summary and outline 9
1.2 The burden of migraine 10
1.2.1 Patient viewpoint 10
1.2.2 Epidemiological viewpoint 14
1.3 Anti-migraine therapy 17
1.3.1 Acute therapy 17
1.3.2 Prophylaxis 20
1.4 Clinical trials of acute anti-migraine drugs 21
1.4.1 Clinical endpoints 21
1.4.2 Timing of treatment 23
1.4.3 Patient demographics 23
1.4.4 Placebo response 24
1.5 Analysis of data from trials of acute anti-migraine drugs 25
1.5.1 Change from baseline 25
1.5.2 Time-to-event analysis 26
1.5.3 Proportional odds models 26
1.5.4 Multistate Models 27
2 Scope and intent of investigation 35
2.1 Scope 35
2.2 Intent of investigation 37
3 Prediction of headache response after migraine treatment using a Markov
model 41
3.1 Introduction 42
3.2 Methods 43
3.2.1 Efficacy data 43
3.2.2 Pharmacokinetic data 43
3.2.3 Markov model 43
3.3 Results 45
3.4 Discussion 46
4 A model-based approach to treatment comparison in acute migraine. 53
4.1 Introduction 54
4.2 Methods 55
4.2.1 Migraine attack model 55
4.2.2 Covariates 56
4.2.3 Data 57
4.2.4 Pharmacokinetic analysis 57
4.2.5 Disease Modelling 58
4.2.6 Model evaluation and prediction 58
4.2.7 Software 58
4.3 Results 60
4.4 Discussion 63
5 The relevance of absorption rate and lag time to the onset of action and pain
relief in migraine 71
5.1 Introduction 72
5.2 Materials and Methods 72
5.2.1 Pharmacokinetic model 72
5.2.2 Response model 74
5.2.3 Model fitting 75
5.2.4 Evaluation of model performance 75
5.3 Results 75
5.3.1 Absorption rate 75
5.3.2 Lag time 77
5.4 Discussion 77
6 Model-based quantification of the relationship between age and anti-migraine
therapy 85
6.1 Introduction 86
6.2 Methods 87
6.2.1 Markov model 87
6.2.2 Age and treatment effects 88
6.2.3 Data 89
6.2.4 Pharmacokinetic analysis 89
6.2.5 Disease Modelling 91
6.2.6 Software 91
6.3 Results 91
6.4 Discussion 91
7 Prediction of attack frequency in migraine:
a Markov approach 97
7.1 Introduction 98
7.2 Methods 99
7.2.1 Data 99
7.2.2 Distribution analysis 99
7.2.3 Stochastic process 100
7.2.4 Goodness-of-fit statistics 101
7.3 Results 102
7.4 Discussion 107
8 Modelling of the PK-PD relationship of anti-migraine drugs using a Markov approach:
Summary, conclusions and perspectives 111
8.1 Developing a disease-state approach to modelling 112
8.2 Development of diagnostic tools 114
8.3 Model consistency across drugs 114
8.4 The effect of covariates on the anti-migraine
response 115
8.5 The episodic nature of migraine 116
8.6 Perspectives 117
8.7 Extensions to the techniques 118
A Appendix:
Analysis of responses in migraine modelling using hidden Markov models 121
A.1 Introduction 122
A.2 Methods 125
A.2.1 Model 125
A.2.2 Predictions 128
A.2.3 Mean responses 128
A.2.4 Confidence intervals 130
A.2.5 Performance of the algorithm 132
A.3 Results 132
A.4 Discussion 134
B Appendix:
Parameter estimation in hidden Markov modelling of migraine 141
B.1 Model specifications 141
B.2 The Baum-Welch algorithm 143
B.3 Model implementation: user-written routines 144
Samenvatting 157
Nawoord 165
Curriculum Vitae 167
List of publications 169
